MATHS 1 Marks Question

p ⟷ q: The unit digit of on integer is zero, if and only if it is divisible by 5.

Let p: 35 is a prime number.
q: 35 is a composite number.
Then, the negation of the given compound statement is:
~(p v q): 35 is not a prime number and it is not a composite number.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

p: Chandigarh is Capital of Haryana.
q: Chandigarh is Capital of U.P.

We know that is either true or false but not both simultaneously.
It is false. Hence, it is a statement.

Cow does not have four legs.

p only if q ⇒ If you do not study, then you will fail.

If x is nether positive nor negative then x = 0.

There exist similar triangles which are not congruent.

If tomorrow is Tuesday, then today is Monday.

If 2x = 3y then x : y = 3 : 2.

q if p ⇒ If take the dinner, then you will get sweet dish.

2 + 7 ≠ 6.

p: 100 is divisible by 3.
q: 100 is divisible by 11.
r: 100 is divisible by 5.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

We know that is either true or false but not both simultaneously.
It is true. Hence, it is a statement.

If the triangle is equilateral, then all three angles of the triangle are equal.

Violet are not blue.

We know that is either true or false but not both simultaneously.
It is false. Hence, it is a statement.

Every real number is not an irrational number.

p: Chennai is in India.
q: Chennai is the Capital of Tamil Nadu.

The weather will not be cold, if it does not snow.

p is sufficient for q ⇒ If an integer is divisible by 5, then its unit digits are 0 or 5.

If you must visit Taj Mahal, then you go to Agra.

Let p: All rational numbers are real.
q: All rational numbers are complex.
~p: All rational numbers are not real.
~q; All rational numbers are not complex.
Then, the negation of the given compound statement is:
~(p ∧ q): All rational numbers are not real or not complex.
[~(p ∧ q) = ~p v ~ q]

Let p: All real numbers are rationals.
q: All real numbers are irrationals.
Then, the negation of the given compound statement is:
~(p v q): All real numbers are not rational and all real numbers are not irrational.
[~(p v q) = ~p ∧ ~ q]

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

If the rectangle R is rhombus, then it is square.

We know that is either true or false but not both simultaneously.
It is true. Hence, it is a statement.

If the triangle is not equilateral, then all three sides of the triangle are not equal.

p: Rahul passed in Hindi.
q: Rahul passed in English.
p ∧ q: Rahul passed in Hindi and English.

p: x = 2 is a root of 3 × 2 - x - 10 = 0.
q: x = 3 is a root of 3 × 2 - x - 10 = 0.
p v q: Either x = 2 or x = 3 i s a root of 3 × 2 - x - 10 = 0.

p: Number 7 is prime.
q: Number 7 is odd.

We know that is either true or false but not both simultaneously.
It is true. Hence, it is a statement.

We know that is either true or false but not both simultaneously.
It is true. Hence, it is a statement.

We know that is either true or false but not both simultaneously.
Since it is a question. Hence, it is not a statement.

2 is a prime number.

p: Two line is a plane intersect at one point.
q: Two lines in a plane are parallel.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

If p, then q ⇒ If the number is odd, then its square is odd number.

Let p: 6 is divisible by 2.
q: 6 is divisible by 3.
Then, the negation of the given compound statement is:
~(p ∧ q): 6 is not divisible by 2 or it is not divisible by 3

Let p:|x| is equal to x.
q:|x| is equal to -x.
Then, the negation of the given compound statement is:
~(p v q): |x| is not equal to JC and it is not equal to -x.

If x 2 > 1 then x is not a real number such that 0 < x < 1.

If the ratio of corresponding sides of two triangles are equal, then triangles are similar.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

p: x is even integers.
q: y is even integers.
p ∧ q: x andy are even integers.

Let p; x = 2 is root of quadratic equation x² - 5x + 6 = 0.
q: x = 3 is root of quadratic equation x² - 5x + 6 = 0.
Then, the negation of the given compound statement is:
~(p ∧ q): x = 2 is not a root of quadratic equation x² - 5x + 6 = 0 or x = 3 is not a root of the quadratic equation x² – 5x + 6 = 0.

We know that is either true or false but not both simultaneously.
It is false. Hence, it is a statement.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
For every.

We know that is either true or false but not both simultaneously.
y + 9 = 7, here that the value of y is not given. So it is true for y = -2 and false for any other value of y. Hence, it is not a statement.

p: Students can take Hindi as an optional paper.
q: Students can take English as an optional paper.
p v q: Students can take Hindi or English as an optional paper.

If x ≠ 3, then x ≠ y or y ≠ 3.

Let p: A triangle has 3-sides.
q: A triangle has 4-sides.
Then, the negation of the given compound statement is:
~(p v q): A triangle has neither 3-sides nor 4-sides.

Here the given statement is the form p q which has the truth value T whenever either p or q or both have the truth value T. Hence, it is a true statement and its component statements are
p: 57 is divisible by 2. (False).
q: 57 is divisible by 3. (True).

p ⟷ q: A natural number is odd if and only if it is not divisible by 2.

If natural number ‘n’ is not divisible by 2 or 3, then n is not divisible by 6.

Area of a circle is not same as the perimeter of the circle.

A leap year does not have 366 days.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
For all.

q implies p ⇒ If a, b, c are in A.P then 2b = a + c.

p: 2 is factor of 12.
q: 3 is factor of 12.
r: 6 is factor of 12.
p ∧ q ∧ r: 2, 3 and 6 are factors of 12

We know that is either true or false but not both simultaneously.
It is false. Hence, it is a statement.

p: 0 is less than every positive integer.
q: 0 is less than every negative integer.

Let p: All prime integers are even.
q: All prime integers are odd.
Then, the negation of the given compound statement is given by ~ (p v q):
All prime integers are not even and all prime integers are not odd.

p: x is an odd integer.
q: (x + 1) is an odd integer.
p v q: Either x or (x + 1) is an odd integer.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
For all.

p: A number is divisible by 2.
q: A number is divisible by 3.
p v q: A number is either divisible by 2 or 3.

If xy is not positive integer, then x or y is not negative integer.

If n is not an integer, then it is not a natural number.

q is necessary for p ⇒ If any number is prime, then its square is not prime.

p ⟷ q: A triangle is an equilateral triangle if and only if all three sides of triangle are equal.

The number 17 is not prime.

p: Plants use sunlight for photosynthesis.
q: Plants use water for photosynthesis.
r: Plants use carbon-dioxide for photosynthesis.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
For all.

If the opposite angles of a quadrilateral are supplementary, then S is cyclic.

p: A rectangle is a quadrilateral.
q: A rectangle is a 5-sides polygon.

If the triangle is right triangle, then the sum of the squares of two sides of a triangle is equal to the square of third side.